Change pivot or local origin of an object
One way to do this is by entering Edit mode and placing the 3D cursor where you want the new origin. (When doing this, you can be very precise by selecting vertices, edges or faces and using them as guides. If you pick several points and snap the cursor to them using Shift+S → Cursor to Selected, Blender will use the average of the selected points to determine the new location of the cursor).

You then go back to Object mode and use Ctrl+Alt+Shift + C → Origin to 3D Cursor to update or change the object origin to the location of the 3D cursor.
For 2.9+ you need to go to Object Menu, and select Set Origin &gt; Origin to 3D Cursor.